Can there be too many bikes in a city for safety? It's not a question usually asked: the received wisdom, supported by research and backed by campaigning groups, is that the more cyclists there are, the safer the roads become for everyone.

But in Copenhagen – one of the most bike-friendly cities in the world in which 36% of its inhabitants cycle to work or school, and which has committed to increasing that figure to 50% by 2015 – there are controversial voices coming from unexpected places.

According to the Danish Cyclists' Federation and Wonderful Copenhagen, the official tourism organisation for Denmark, the sheer success of the drive to get more locals and tourists on bikes is creating a dangerous, intimidating and unpleasant climate for cyclists in the city.

"In Copenhagen, we have quite extraordinary problems around cycling congestion," said Aneh Hajdu, of Wonderful Copenhagen. "I don't take my children on their bikes into Copenhagen at rush hour any more. It's too dangerous and scary. I just wouldn't risk it."

It is not just the locals who are, according to Hajdu, finding the sheer crush of cyclists in Copenhagen an ordeal. "I went on a cycling trip around Copenhagen with a friend visiting from London recently, and she was terrified by the mass of cyclists and the aggressive way they behaved," said Hadju. "She found them so overwhelming that she burst into tears. She was too scared to get back on her bike. We had to put it in a taxi and drive back home."

As numbers increase in the cycle lanes, says Hadju, so behaviour deteriorates, with jostling and cutting-up becoming more frequent. "The locals rush past the foreigners, who are often uncertain on their bikes and going slowly," she said. "The locals get impatient and therefore become more threatening."

Even to an untrained eye, it is immediately obvious that the city is struggling to cater for its growing number of cyclists. It is already near-impossible to find cycling parking places near main stations, while cycling lanes that seem gargantuan to British eyes – three to four meters wide compared to our 1.5 meters – are buried at certain times of day beneath the scrum of cyclists traversing the city.

So what happens when the critical mass of cyclists grows faster than the government can improve their uban environment?

Frits Bredal, of the Danish Cyclists' Federation acknowledges that the number of serious traffic accidents involving cyclists in Copenhagen has reduced dramatically in the last few years and that the numbers of cyclists killed is at a historic low.

But he fears a turnaround in the statistics: "In rush hour, there are enormous numbers of cyclists fighting for space on Copenhagen's bike paths, which become cramped and packed.

"As numbers grow and they fight for space, cyclists are becoming more aggressive and reckless in traffic. I increasingly see people bringing themselves and others into dangerous situations," he adds. "They break the laws and use their bikes in completely reckless ways."

The knock-on effect of such behaviour is, Bredal says, damaging the cause of campaigners trying to persuade the government to increase the width and number of cycle paths, and introduce multi-storey bike parking facilities.

"Their behaviour means that the politicians say, which is fair enough, that before they give the city more bike paths, we have a job for ourselves to get the cyclists we already have, to behave," he says.

Others, however, are frustrated by such claims. MikaelColville-Andersen, Denmark's unofficial ambassador for cycling thanks to his Copenhagenize and Copenhagen Cycle Chic blogs) even fears they could undermine the pro-cycling atmosphere in Copenhagen that he and so many others have worked hard to create. "It's true that cycling in Copenhagen in the rush hour is not for the faint-hearted: it requires concentration and it's true that we do need wider lanes," he says."But it's not as dangerous as the DCF like to say. Statistics provethat it's safer than Amsterdam.".

"The Danish Cyclists' Federation are trying to advocate for more and better bike lanes by saying it's dangerous to cycle with the situation as it now is," he adds. "But by telling people that cycling is dangerous, they're shooting themselves in the foot. They need to think about encouraging urban cycling as being a product, like any other, that you want to sell. That means you need to emphasise its positive aspects.

"We should make urban cycling positive like we do every other product we want to encourage people to buy," he says, pointing towards research by the European Cyclists' Federation. This says:

There are a number of examples of cities, where a substantial increase in bicycle use has been associated with a decrease in the number of cycling accidents. In the positive health impact from the physical exercise is taken into account, cycling will in any case be beneficial for the user.